Rigorous Mathematics Instruction in Middle School Weekend 1: Planning and Teacher Preparation Kendra Heinricher 8 th Grade Math Teacher and Network Mathematics Department Head Excel Academy Charter Schools Kaitlyn Giles Dean of Curriculum and Instruction (Former 5 th Grade Math Teacher) Excel Academy – Orient Heights

Agenda for the Day I.Clarifying Beliefs and Setting a Vision II.Planning and Preparation III.Work Time

Guiding Session Questions As a teacher committed to our ambitious mission, how do I develop aligned, rigorous math materials that prompt student thinking? or As an instructional leader committed to our ambitious mission, how do I support teachers in the development of aligned, rigorous materials that prompt student thinking?

Clarifying Your Beliefs about Teaching and Learning Math What does it mean to do math? What does it mean to know math? What does success look like in math? What does a rigorous math class look like? Sound like? Feel like? What teaching practices support those measures? Are your beliefs aligned with other math teachers at your grade level? In your school? In your network?

Planning and Preparation Overview 1.Breaking down standard/objective 2.Establishing core concept/key takeaways 3.Choosing lesson structure 4.Creating materials that drive lesson 5.Providing scaffolding and organizers 6.Formatting for student thinking and doing

1. Breaking down standard/objective What key concepts are involved in that standard? Why is it important for students to know? What knowledge are they bringing into this lesson? To what depth have they covered this objective in previous years? What is brand new? What will they need to have previewed?

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Underlying concept is common multiple as common denominator. PARCC does not specify whether an answer is in simplest form though there is emphasis on equivalent sums and differences. Common Core pushes beyond sums of a whole. 5 th grade model SWBAT add and subtract fractions with uncommon denominators.

8.EE.8B Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. MCAS and PARCC do not prescribe HOW to solve a system in a given problem. Students need to have a variety of strategies and be flexible in their thinking based on the numbers in the equations. 8 th grade model SWBAT solve systems of linear equations by elimination.

Group Practice Comparing and ordering mixed sets of numbers 5 th -6 th grade: sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers 6.NS.7 Understand ordering and absolute value of rational numbers. a.Interpret statements of inequality as statements about the relative positions of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b.Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 o C > –7 o C to express the fact that –3 o C is warmer than –7 o C.

Group Practice Comparing and ordering mixed sets of numbers What key concepts are involved in that standard? Why is it important for students to know? What knowledge are they bringing into this lesson? To what depth have they covered this objective in previous years? What is brand new? What will they need to have previewed? 5 th -6 th grade: sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers

2. Establishing core concept/key takeaways What are the key points embedded in this objective? What discrete skills should students have at the end of this lesson? What are the takeaways at the end of this lesson to gauge student mastery? What should students be able to articulate? Visible thinking What should students be able to show?

5 th grade model SWBAT add and subtract fractions with uncommon denominators.

8 th grade model SWBAT solve systems of linear equations by elimination.

Group Practice Comparing and ordering mixed sets of numbers 5 th -6 th grade: sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers What are the key points embedded in this objective? What discrete skills should students have at the end of this lesson? What are the takeaways at the end of this lesson to gauge student mastery? What should students be able to articulate? Visible thinking What should students be able to show?

3. Choosing a lesson structure How do I present this to students to put the maximum amount of cognitive load onto them? Direct instruction with procedural practice Inquiry based Within that framework, what are the main tools or teaching strategies involved? Modeling Manipulatives Visuals

5 th grade model SWBAT add and subtract fractions with uncommon denominators. What information do I need to provide to students? What is the necessary balance between concept and procedure? How do I show them the why? How do I want them to practice?

8 th grade model SWBAT solve systems of linear equations by elimination. What questions should I ask to activate student knowledge? How do I sequence questions to move students towards the understandings I want them to have? When/how do we formalize the process?

Group Practice Comparing and ordering mixed sets of numbers 5 th -6 th grade: sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers How do I present this to students to put the maximum amount of cognitive load onto them? Direct instruction with procedural practice Inquiry based Within that framework, what are the main tools or teaching strategies involved? Modeling Manipulatives Visuals

WORKING LUNCH with Action Planning

4. Creating materials that drive lesson How can I create material that will make students think and allow them to carry that cognitive load? Am I asking the right questions? How do the questions flow? How will students experience this class?

5 th grade model SWBAT add and subtract fractions with uncommon denominators.

8 th grade model SWBAT solve systems of linear equations by elimination.

Given resources, put together a rough draft of a material based on CONTENT that answers the questions we posed earlier: How does this strike the balance you were looking for? How can I create a material that will make them think and allow them to carry that cognitive load? Are we asking the right questions? How do the questions flow? Group Practice Comparing and ordering mixed sets of numbers 5 th -6 th grade : sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers

5.Scaffolding and organizers How can we support/streamline student thinking? How is an organizer assisting students with the cognitive demand of the lesson?

5 th grade model SWBAT add and subtract fractions with uncommon denominators. Least Common Denominator Transformer TSimplify (rainbow) Circle your final answer x x

8 th grade model SWBAT solve systems of linear equations by elimination.

Is there a structure or organizer that could direct student work output to ensure productive practice? Group Practice Comparing and ordering mixed sets of numbers 5 th -6 th grade: sets can include fractions, decimals, percents 7 th -8 th grade: sets can include repeating decimals, exponents, radicals, scientific notation, negative rational numbers

6. Formatting for student thinking and doing Is there SPACE for students to think and show their thinking? What do I need to put on the page to provide adequate support? How does what is on the page support the learning ?

5 th grade model SWBAT add and subtract fractions with uncommon denominators.

5 th grade model SWBAT add and subtract fractions with uncommon denominators.

8 th grade model SWBAT solve systems of linear equations by elimination.

Supported Work Time Teachers: Use guiding questions to work on materials for an upcoming lesson Coaches: Develop a template that you could use with teachers to assist them in going through this process with materials or look at materials for a lesson you are supporting / have supported.

Outstanding Questions? Kendra Kaitlyn

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